nm

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13 years, 36 days

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These are questions asked by nm

What is the correct idiom in Maple to do subexpression replacement?

Suppose I want to replace each occurance of ln(anything) by ln(abs(anything)) in an expression.

Currently I call indets and then loop over each entry and use patmatch to do the replacement.

Is there a better method than what I doing now? Here is an example

restart;
expr := 7*ln(arcsin(x))-(1/2)*ln(x-1)*sin(x)-(1/2)*ln(x+1)+f;
lis:=indets(expr):
for z in lis do
    a:='a';b:='b';c:='c';
    if patmatch(z,a::anything*ln(b::anything)*c::anything,'la') then
       map(z0->assign(z0),la);
       expr:=subs(z = a*ln(abs(b))*c, expr);
    fi;
od:
expr;

I do not know if this will fails on some other cases yet.

I found that when changing constant of integration from _C1 to C1, Maple now fails to verify solution.

Is one supposed to only use constant with _ in it for this? I prefer to use C1 instead of _C1. Why does Maple odetest fail in this case? Is there a way around this?

Here is an example

restart;
ode:=diff(y(x),x)=x*ln(y(x)):
implicit_sol := -Ei(1, -ln(y(x)))+C1=(1/2)*x^2;
explicit_sol := solve(implicit_sol,y(x)):
odetest(y(x)=explicit_sol,ode);

Now changing C1 to _C1 and nothing else, odetest verifies the solution

implicit_sol:= subs(C1=_C1,implicit_sol);
explicit_sol := solve(implicit_sol,y(x)):
odetest(y(x)=explicit_sol,ode);

I understand the using symbol with _ is a convention in Maple for global symbols. But I want to use C1 and not _C1 as it is easier to read.

 

I want to check that all entries in a list are of some value. Say 0. (or in general, if all entries satisfy some condition).

So, If any entry is not zero, then it returns false. It returns true only if all elements meet this conditions.

What would be the right way to do this in Maple? I know I could write a loop. But I am asking if there is a build-in function in Maple. Here is an example

ode:=y(x)*diff(y(x),x)=x*(y(x)^2+2):
sol:= dsolve(ode,y(x)):
check:=map(z->odetest(z,ode1),[sol]);

                       check := [0, 0]

I want to check that all entries in check are zero. This tells me all my solution are correct.

I can't use member(check,0) since this only check if at least one entry is zero. I want to chek that all entries are zero.

In Mathematica, it has AllTrue function. Like this

check = {0, 0, 0};
AllTrue[check, # == 0 &]

     True

The "#==0&"  is the test to do. It uses this test on each element automatically. If all satisfy this test, then it returns true.

Again, I can easily write a small function in Maple to do this,

alltrue :=proc(arr,value)
    local z;
    for z in arr do
        if z<>value then
           return(false);
        fi;
    od;
    return(true);
end proc:

alltrue(check,0) return true.

But I am asking if there is a build-in such function similar to the above one in Mathematica, which accepts a more general test function to use.

why

expr:=1-3*y;
patmatch(expr, b::integer - a::integer*y,'la');

gives false but

expr:=1-3*y;
patmatch(expr, b::integer + a::integer*y,'la');

gives true?

Should one then use `+` for matching with `+` and `-`? This result was a little confusing to me. 

It is actually good that it behaves this way. Makes it easier to write the pattern (less cases to cover). But I would have expected both to return true, that is all.

I found I can start Maple itself 2 times on my windows PC. (I think my license allows max of 2, but I could be wrong).

I want to run a program which takes long time. But I want to use Maple at same time.

Which is the recommended approach:

1) Start 2 separate Maple applications. Use one to run the long program, and then I can use the second Maple for other things while the first is running)

2) Start one Maple, but set the "How should Maple handle the create of new Math engine" to "Ask me each time"

for me, choice 1 seems more safe. But thought to ask if there is something else I should consider when making which choice to pick.

Update

Found out that actually when clicking on Maple icon, I was not starting a new Maple at all. It was just starting a new worksheet using the currently running Maple ! This is confusing. With Mathematica, clicking on its icon actually starts a new complete separate Mathematica application. Not a new notebook using the currently running Mathematica.

So the question I have now is: Can one start 2 separate Maple applications on windows?  And if so, how?

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